[1]
Tom M. Apostol, Introduction to analytic number theory, Undergraduate Texts in Mathematics, Springer-Verlag, New York-Heidelberg, (1976). MR434929.
References Bibliography
[2]
Michael Artin, Algebra, Prentice Hall, Inc., Englewood Cliffs, NJ, (1991). MR1129886. 0-13-004763-5.
[3]
M. F. Atiyah and I. G. Macdonald, Introduction to commutative algebra, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., (1969). MR242802.
[4]
Armand Borel, Cohomologie de \({\rm SL}_{n}\) et valeurs de fonctions zeta aux points entiers, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 4 no. 4 613–636, (1977). MR506168. http://www.numdam.org/item?id=ASNSP_1977_4_4_4_613_0. 0391-173X,2036-2145.
[5]
Kenneth S. Brown, Euler characteristics of discrete groups and \(G\)-spaces, Invent. Math. 27 229–264, (1974). MR385007. https://doi.org/10.1007/BF01390176. 0020-9910,1432-1297.
[6]
Laurent Clozel, Formes modulaires modulo p, changement de base et théorie d’iwasawa, HAL 2014 (2014). http://dml.mathdoc.fr/item/hal-00957919. fr.
[7]
Laurent Clozel, Formes modulaires sur la \(\mathbb Z_p\)-extension cyclotomique de \(\mathbb Q\), Pacific J. Math. 268 no. 2 259–274, (2014). MR3227435. https://doi.org/10.2140/pjm.2014.268.259. 0030-8730,1945-5844.
[8]
J. Coates and R. Sujatha, Cyclotomic fields and zeta values, Springer Monographs in Mathematics, Springer-Verlag, Berlin, (2006). MR2256969. 978-3-540-33068-4; 3-540-33068-2.
[9]
John Coates, On \(K_{2}\) and some classical conjectures in algebraic number theory, Ann. of Math. (2) 95 99–116, (1972). MR360523. https://doi.org/10.2307/1970857. 0003-486X.
[10]
John Coates, Kenkichi iwasawa (1917-1998), Notices of the AMS 46 no. 10 1221–1225, (1999).
[11]
Richard Dedekind, Über die Theorie der ganzen algebraischen Zahlen, Friedr. Vieweg & Sohn, Braunschweig, (1964). MR175878. Mit einem Geleitwort von B. van der Waerden.
[12]
PG Lejeune Dirichlet, Proof of the theorem that every infinite arithmetic progression whose first term and difference are integers without a common factor contains infinitely many prime numbers, Treatises of the Royal Prussian Academy of Sciences 45 81, (1837).
[13]
L. Euler, Variae observationes circa series infinitas, Commentarii academiae scientiarum Petropolitanae 9 160–188, (1744).
[14]
Eberhard Freitag and Reinhardt Kiehl, Étale cohomology and the Weil conjecture, 13 Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], Springer-Verlag, Berlin, (1988). MR926276. https://doi.org/10.1007/978-3-662-02541-3. 3-540-12175-7. Translated from the German by Betty S. Waterhouse and William C. Waterhouse, With an historical introduction by J. A. Dieudonné.
[15]
Eric M. Friedlander and Daniel R. Grayson (ed.), Handbook of \(K\)-theory. Vol. 1, 2, Springer-Verlag, Berlin, (2005). MR2182598. https://doi.org/10.1007/3-540-27855-9. 978-3-540-23019-9; 3-540-23019-X.
[16]
William Fulton and Joe Harris, Representation theory, 129 Graduate Texts in Mathematics, Springer-Verlag, New York, (1991). MR1153249. https://doi.org/10.1007/978-1-4612-0979-9. 0-387-97527-6; 0-387-97495-4. A first course, Readings in Mathematics.
[17]
Fernando Q. Gouvêa, \(p\)-adic numbers. an introduction, Universitext, Springer, Cham, (2020). MR4175370. https://doi.org/10.1007/978-3-030-47295-5. 978-3-030-47295-5; 978-3-030-47294-8. Third edition.
[18]
G. Harder, A Gauss-Bonnet formula for discrete arithmetically defined groups, Ann. Sci. École Norm. Sup. (4) 4 409–455, (1971). MR309145. http://www.numdam.org/item?id=ASENS_1971_4_4_3_409_0. 0012-9593.
[19]
Kenneth Ireland and Michael Rosen, A classical introduction to modern number theory, 84 Graduate Texts in Mathematics, Springer-Verlag, New York, (1990). MR1070716. https://doi.org/10.1007/978-1-4757-2103-4. 0-387-97329-X. Second edition.
[20]
Kenkichi Iwasawa, Some properties of \(L\)-groups, Proceedings of the International Congress of Mathematicians, Cambridge, Mass., 1950, vol. 2 Amer. Math. Soc., Providence, RI, 447–450, (1952). MR44534.
[21]
Kenkichi Iwasawa, On \(\Gamma \)-extensions of algebraic number fields, Bull. Amer. Math. Soc. 65 183–226, (1959). MR124316. https://doi.org/10.1090/S0002-9904-1959-10317-7. 0002-9904.
[22]
Kenkichi Iwasawa, Analogies between number fields and function fields, Some Recent Advances in the Basic Sciences, Vol. 2 (Proc. Annual Sci. Conf., Belfer Grad. School Sci., Yeshiva Univ., New York, 1965-1966) Yeshiva University, Belfer Graduate School of Science, New York, 203–208, (1969). MR255510.
[23]
Kenkichi Iwasawa, On \(p\)-adic \(L\)-functions, Ann. of Math. (2) 89 198–205, (1969). MR269627. https://doi.org/10.2307/1970817. 0003-486X.
[24]
Kenkichi Iwasawa, Lectures on \(p\)-adic \(L\)-functions, No. 74 Annals of Mathematics Studies, Princeton University Press, Princeton, NJ; University of Tokyo Press, Tokyo, (1972). MR360526.
[25]
Qingzhong Ji and Hourong Qin, Iwasawa theory for \(K_{2n}\mathscr{O}_F\), J. K-Theory 12 no. 1 115–123, (2013). MR3126637. https://doi.org/10.1017/is013004020jkt225. 1865-2433,1865-5394.
[26]
Neal Koblitz, \(p\)-adic numbers, \(p\)-adic analysis, and zeta-functions, Vol. 58 Graduate Texts in Mathematics, Springer-Verlag, New York-Heidelberg, (1977). MR466081. 0-387-90274-0.
[27]
Ernst Eduard Kummer, Collected papers, Springer-Verlag, Berlin-New York, (1975). MR465760. Volume I: Contributions to number theory, Edited and with an introduction by André Weil.
[28]
Serge Lang, Algebra, 211 Graduate Texts in Mathematics, Springer-Verlag, New York, (2002). MR1878556. https://doi.org/10.1007/978-1-4613-0041-0. 0-387-95385-X. third edition.
[29]
Daniel A. Marcus, Number fields, Universitext, Springer, Cham, (2018). MR3822326. https://doi.org/10.1007/978-3-319-90233-3. 978-3-319-90232-6; 978-3-319-90233-3. With a foreword by Barry Mazur. Second edition.
[30]
Barry Mazur and Andrew Wiles, Class fields of abelian extensions of q, Inventiones mathematicae 76 179–330, (1984). https://api.semanticscholar.org/CorpusID:122576427.
[31]
Hugh L. Montgomery and Robert C. Vaughan, Multiplicative number theory i: Classical theory, Cambridge Studies in Advanced Mathematics, Cambridge University Press, (2006).
[32]
M. Ram Murty and V. Kumar Murty, Non-vanishing of \(L\)-functions and applications, 157 Progress in Mathematics, Birkhäuser Verlag, Basel, (1997). MR1482805. https://doi.org/10.1007/978-3-0348-0274-1. 3-7643-5801-7.
[33]
Gabriel Navarro, Character theory and the McKay conjecture, 175 Cambridge Studies in Advanced Mathematics, Cambridge University Press, Cambridge, (2018). MR3753712. https://doi.org/10.1017/9781108552790. 978-1-108-42844-6.
[34]
Jürgen Neukirch, Algebraic number theory, 322 Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], Springer-Verlag, Berlin, (1999). MR1697859. https://doi.org/10.1007/978-3-662-03983-0. 3-540-65399-6. Translated from the 1992 German original and with a note by Norbert Schappacher, With a foreword by G. Harder.
[35]
Dipendra Prasad, A mod-\(p\) Artin-Tate conjecture, and generalizing the Herbrand-Ribet theorem, Pacific J. Math. 303 no. 1 299–316, (2019). MR4044864. https://doi.org/10.2140/pjm.2019.303.299. 0030-8730,1945-5844.
[36]
M. Ram Murty, Introduction to \(p\)-adic analytic number theory, 27 AMS/IP Studies in Advanced Mathematics, American Mathematical Society, Providence, RI; International Press, Somerville, MA, (2002). MR1913413. https://doi.org/10.1090/amsip/027. 0-8218-3262-X.
[37]
Bernhard Riemann, Ueber die anzahl der primzahlen unter einer gegebenen grösse, Monatsberichte der Königlich Preußischen Akademie der Wissenschaften zu Berlin (1859).
[38]
Alain M. Robert, A course in \(p\)-adic analysis, 198 Graduate Texts in Mathematics, Springer-Verlag, New York, (2000). MR1760253. https://doi.org/10.1007/978-1-4757-3254-2. 0-387-98669-3.
[39]
Steven Roman, Fundamentals of group theory, Birkhäuser/Springer, New York, (2012). MR2866265. https://doi.org/10.1007/978-0-8176-8301-6. 978-0-8176-8300-9. An advanced approach.
[40]
Michael Rosen, Number theory in function fields, 210 Graduate Texts in Mathematics, Springer-Verlag, New York, (2002). MR1876657. https://doi.org/10.1007/978-1-4757-6046-0. 0-387-95335-3.
[41]
Jean-Pierre Serre, Cohomologie des groupes discrets, Prospects in mathematics (Proc. Sympos., Princeton Univ., Princeton, N.J., 1970) No. 70 Ann. of Math. Stud., Princeton Univ. Press, Princeton, NJ, 77–169, (1971). MR385006.
[42]
Jean-Pierre Serre, Linear representations of finite groups, Vol. 42 Graduate Texts in Mathematics, Springer-Verlag, New York-Heidelberg, (1977). MR450380. 0-387-90190-6. French edition.
[43]
Jean-Pierre Serre, Local fields, 67 Graduate Texts in Mathematics, Springer-Verlag, New York-Berlin, (1979). MR554237. 0-387-90424-7. Translated from the French by Marvin Jay Greenberg.
[44]
Joseph H. Silverman, The arithmetic of elliptic curves, 106 Graduate Texts in Mathematics, Springer-Verlag, New York, (1992). MR1329092. 0-387-96203-4. Corrected reprint of the 1986 original.
[45]
J. T. Tate, Fourier analysis in number fields, and Hecke’s zeta-functions, Algebraic Number Theory (Proc. Instructional Conf., Brighton, 1965) Academic Press, London, 305–347, (1967). MR217026.
[46]
H. S. Vandiver, Fermat’s last theorem. Its history and the nature of the known results concerning it, Amer. Math. Monthly 53 555–578, (1946). MR18660. https://doi.org/10.2307/2305236. 0002-9890,1930-0972.
[47]
L.C. Washington, Introduction to cyclotomic fields, Graduate Texts in Mathematics, Springer New York, (1997). https://books.google.co.uk/books?id=qea_OXafBFoC. 9780387947624.
[48]
André Weil, Scientific works. Collected papers. Vol. I (1926--1951), Springer-Verlag, New York-Heidelberg, (1979). MR537937. 0-387-90330-5.
[49]
A. Wiles, The Iwasawa conjecture for totally real fields, Ann. of Math. (2) 131 no. 3 493–540, (1990). MR1053488. https://doi.org/10.2307/1971468. 0003-486X,1939-8980.
